Delaying the Catastrophic Arrival of the Brown Tree Snake to Hawaii

This paper develops a two-stage model for the optimal management of a potential invasive species. The arrival of an invasive species is modeled as an irreversible event with an uncertain arrival time. The model is solved in two stages, beginning with the post-invasion stage. In this stage, we assume perfect certainty regarding population size and arrivals. The loss-minimizing paths of prevention and control are identified, resulting in a minimized present value penalty associated with the invasion. After calculating this penalty, we analyze the pre-invasion stage and solve for the level of prevention expenditures that will minimize expected total cost. For the case of the Brown Tree Snake potentially invading Hawaii, we find that under a regime of precommitment, pre-invasion expenditures on prevention should be approximately $3.2 million today, decreasing every year until invasion. However, if the planner is permitted to re-evaluate the threat following a non-event, prevention will be lower ($2.96 million a year) and constant until invasion. Once invasion occurs, optimal management requires lower annual expenditures on prevention ($3.1 million) but requires $1.6 million to be spent on control annually to keep the population at its steady state level.